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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 1 (25 MCQs)

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1. If C(x) = 500 + 20x, the marginal cost MC(x) is:
2. If the position of a particle is represented by x(t) =-t$^{2}$ + 1, what is its instantaneous velocity at t = 1?
3. Find the third derivative of the function:f (x) = 2x-5x$^{6}$
4. Find $k^{" }\left(x\right)$ $k\left(x\right)=8x^{-3}-24x^{-2}+12x^{-1}$
5. The function f has a first derivative $f'\left(x\right)=x\left(x-3\right)^2\left(x+1\right)$
6. We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.
7. If a function switches from increasing to decreasing, what occurs between?
8. Identify the conclusion of Rolle's Theorem.
9. An objects distance from its starting point at time t is given by the equation s(t) = t$^{3}$-6t$^{2}$-4. What is the speed of the object when its acceleration is 0?
10. The function f(x) = x + cos x is
11. If f' > 0 on an interval, then f is increasing on that interval.
12. If the first derivative of a function changes from positive to negative at a certain point, then that point is a known as a relative minimum.
13. Given x(t)=t$^{3}$-4t$^{2}$+7, what is the initial position?
14. The demand function D(p)=120-3p. At price p=10, the elasticity of demand is:
15. If f '(x) >0, what is true about f(x)?
16. If $f'\left(x\right)=\sqrt{2x^2-1}$ $y=f\left(x^2\right), $ $\frac{dy}{dx}$
17. Find the x-coordinate of the inflection point of f(x)=6x$^{2}$-x$^{3}$.
18. When f ''(x) changes from negative to positive, there is
19. Using the tangent line approximation for $f\left(x\right)=\sqrt{x}$ $\sqrt{8.2}$
20. To find the velocity function, you need the
21. If fixed costs increase but marginal cost function MC(x) is unchanged, the marginal cost curve shifts upward.
22. What is the differential equation, $dy=f'(x)dx$ $\sqrt{52}$
23. Does y =-4x$^{2}$ have a maximum or minimum value?
24. If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?
25. A rectangular page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper
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